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A190099 Number of 1:2:sqrt(5) proportioned triangles on an (n+1) X (n+1) grid. 2

%I #11 May 04 2018 22:40:54

%S 0,16,64,176,384,744,1288,2104,3224,4776,6784,9408,12672,16776,21736,

%T 27792,34944,43488,53400,65032,78336,93720,111112,130976,153216,

%U 178360,206272,237552,272024,310368,352360,398752,449280,504776,564928,630648

%N Number of 1:2:sqrt(5) proportioned triangles on an (n+1) X (n+1) grid.

%C Diagonal of A190100.

%H R. H. Hardin, <a href="/A190099/b190099.txt">Table of n, a(n) for n = 1..103</a>

%F Empirical: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) +a(n-5) -3*a(n-6) +3*a(n-8) -a(n-9) +2*a(n-11) -2*a(n-12) -a(n-13) +a(n-14).

%F Empirical g.f.: 8*x^2*(2 + 2*x + 2*x^2 + 2*x^3 + x^4)*(1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4) / ((1 - x)^5*(1 + x)^3*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, May 04 2018

%e Some solutions for n=5:

%e 3 0 3 2 5 0 2 0 1 2 5 5 3 5 3 0 2 3 0 4

%e 1 0 2 1 3 0 1 1 1 0 1 5 2 4 2 1 0 3 1 5

%e 3 1 5 0 5 1 4 2 5 2 5 3 5 3 5 2 2 2 2 2

%Y Cf. A190100.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 04 2011

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